Dense medium phase and amplitude correction theory for spatially and electrically dense media

The conventional scattering phase matrix is developed based on the assumption that the scatterers are in the far field of one another. In an electrically dense medium where there is more than one scatterer within the distance of a wavelength, this approximation no longer holds. Generally two types of corrections are necessary: the amplitude and the phase correction. In this paper, a new phase matrix for a volume of densely packed discrete random spherical scatterers is discussed. This phase matrix differs from the conventional one in that both amplitude and phase corrections are included. By invoking the antenna array concept, the phase matrix is found to be the Stokes matrix of the single scatterer multiplied by a dense medium phase correction factor. The amplitude correction due to close-spacing appears in the Stokes matrix. Using this phase matrix, the volume scattering coefficient of a unit volume of spherical scatterers is calculated. The backscattering coefficients from a layer of spherical scatterers are also calculated based on the matrix doubling formulation. This study shows that phase coherency and close-spacing amplitude modifications are two separate corrections necessary for an electrically dense medium. When the wavelength decreases, both the volume scattering coefficient and the backscatter of the layer approach the usual results under the far-field condition, even though the scatterers are spatially dense. Whether or not a medium behaves as a dense medium in scattering, the incident wavenumber times the average spacing between adjacent scatterers is the important parameter. Thus, there is a need to distinguish between spatially and electrically dense media.